Editing Gini coefficient (section)

== Relation to other statistical measures ==
There is a summary measure of the diagnostic ability of a binary classifier system that is also called the ''Gini coefficient'', which is defined as twice the area between the [[receiver operating characteristic]] (ROC) curve and its diagonal.  It is related to the [[Receiver operating characteristic#Area under the curve|AUC]] ([[Integral|Area Under]] the ROC Curve) measure of performance given by <math>AUC = (G+1)/2</math><ref name=hand>{{cite journal |last1=Hand |first1=David J. |last2=Till |first2=Robert J. |title=A Simple Generalisation of the Area Under the ROC Curve for Multiple Class Classification Problems |journal=Machine Learning |date=2001 |volume=45 |issue=2 |pages=171–186 |doi=10.1023/A:1010920819831 |doi-access=free }}</ref>   and to [[Mann–Whitney U]].  Although both Gini coefficients are defined as areas between certain curves and share certain properties, there is no simple direct relationship between the Gini coefficient of statistical dispersion and the Gini coefficient of a classifier.
 
The Gini index is also related to the Pietra index — both of which measure statistical heterogeneity and are derived from the Lorenz curve and the diagonal line.<ref>{{cite journal|first1=Iddo I.|last1=Eliazar |first2=Igor M.|last2=Sokolov |year=2010 |title=Measuring statistical heterogeneity: The Pietra index|journal=Physica A: Statistical Mechanics and Its Applications|volume=389|issue= 1|pages= 117–125|doi= 10.1016/j.physa.2009.08.006|bibcode=2010PhyA..389..117E}}</ref><ref>{{cite journal |last1=Lee |first1=Wen-Chung |title=Probabilistic analysis of global performances of diagnostic tests: interpreting the Lorenz curve-based summary measures |journal=Statistics in Medicine |date=28 February 1999 |volume=18 |issue=4 |pages=455–471 |doi=10.1002/(sici)1097-0258(19990228)18:4<455::aid-sim44>3.0.co;2-a |pmid=10070686 }}</ref><ref name="McDonald1974"/>

In certain fields such as ecology, inverse Simpson's index <math>1/\lambda</math> is used to quantify diversity, and this should not be confused with the [[Diversity index#Simpson index|Simpson index]] <math>\lambda</math>. These indicators are related to Gini. The inverse Simpson index increases with diversity, unlike the Simpson index and Gini coefficient, which decrease with diversity. The Simpson index is in the range [0, 1], where 0 means maximum and 1 means minimum diversity (or heterogeneity). Since diversity indices typically increase with increasing heterogeneity, the Simpson index is often transformed into inverse Simpson, or using the complement <math>1 - \lambda</math>, known as the Gini-Simpson Index.<ref>{{cite journal|title=The Measurement of Species Diversity|first=Robert K.|last=Peet|s2cid=83517584|journal=Annual Review of Ecology and Systematics|volume=5|year=1974 |issue=1 |pages= 285–307|jstor=2096890|doi=10.1146/annurev.es.05.110174.001441|bibcode=1974AnRES...5..285P }}</ref>

The [[Lorenz curve]] is another method of graphical representation of wealth distribution. It was developed 9 years before the Gini coefficient, which quantifies the extent to which the Lorenz curve deviates from the perfect equality line (with [[slope]] of 1). The [[Hoover index]] (also known as Robin Hood index) presents the percentage of total population's income that would have to be redistributed to make the Gini coefficient equal to 0 (perfect equality).<ref>{{Cite web |title=Hoover Index |url=https://corporatefinanceinstitute.com/resources/economics/hoover-index/ |access-date=2024-04-28 |website=Corporate Finance Institute |language=en-US}}</ref>